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Summary

The following contains summaries of major chapters covered under the H1 and H2 Mathematics syllabus. They are compiled based on my understanding as a student and experience as a tutor, and I hope current JC students will benefit from them.

Lecture notes provide plenty of information, but not all are examinable. I have listed the important points which I highly recommend students to be familiar with. Experience tells me that knowing these points will serve you well for any tests and exams.

These summaries are in secured pdf format i.e. printing, copying and editing rights are excluded.

Pay special attention to Note, Special Note and Other observations within these summaries.

Students are advised to consult your respective teachers on the accuracy of my summaries.

LEGEND:

For H1 students, For H2 students, pdf document

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Summaries for Pure Mathematics Topics

FunctionsDownload/ViewStudents are required to determine whether inverse & composite functions exist, define inverse and composite functions as well as determine the range and domain of these functions. Students must also know how to restrict the domain of the functions when inverse/composite functions do not exist initially. Finally, students must be able to sketch inverse & composite functions using GC and solve problems involving f(x) and its inverse.

Last Updated: Dec 2009

Binomial ExpansionDownload/ViewStudents are required to find the binomial series expansion for equations in the form [1+f(x)]^n, where n is a non-positive integer. Also, students must be able to define the range of values of f(x) for the expansion to be valid and determine the coefficient of x^n when asked. Solving Partial Fraction is usually required.

Last Updated: July 2009

Summation SeriesDownload/ViewStudents are required to remember and apply the properties of summation as well as recall the formulas for the sum of r, r^2 and r^3. Students must be able to identify and simplify a Method of Difference problem. Solving Partial Fraction, inequalities & limits are usually required.

Last Updated: May 2009

Arithmetic & Geometric Progression (APGP)Download/ViewStudents are required to prove that a series is an AP or GP, solve AP GP problems using appropriate formulas and identify if the series is converging or diverging. Students are also required to apply APGP knowledge to solve compound interests and similar application problems.

Last Updated: April 2009

Graphing TechniquesDownload/ViewStudents are required to sketch and define a conic section (i.e. parabola, ellipse, circle, hyperbola), rational functions and other basic functions. Students must know how to determine the asymptotes, turning points as well as all axial intercepts for a rational function. Students are expected to solve problems involving either single or two graphs, using GC or algebraic approach. Also, students must be able to perform graph transformations esp y=1/f(x), y^2=f(x), y=f '(x) & y=f(|x|) etc.

Last Updated: June 2009

IntegrationDownload/ViewStudents are required to evaluate indefinite & definite integrals (i.e. Area). H2 students are required to apply the different techniques of integration such as by partial fractions, standard forms, substitution & by parts. Also, H2 students must know how to define areas in parametric form and solve volume of revolution problems involving single or two curves.

Last Updated: Dec 2009

VectorsDownload/ViewStudents are required to define vector line & plane equations, find intersections between lines and/or planes, apply ratio and mid point theorems. Also, students must be able to solve application problems such as finding length of projection, foot of perpendicular, shortest distance, angles etc.

Last Updated: Aug 2009

DifferentiationDownload/ViewStudents are required to recall the differentiation of various types of functions. Students must be able to solve application problems involving rates of change, maxima & minima and equations of tangent & normal. For H2 students, you must be familiar with the Maclaurin's series expansion.

Summaries for Statistics Topics

Binomial DistributionDownload/ViewStudents are required to identify and denote a binomial distribution, determine the probability using GC, evaluate n & p using either GC or formula if not provided and use E(X)=np, Var(X)=np(1-p). Also, students must know the conditions for using approximations. H2 students must know both Poisson & Normal approximations.

Last Updated: Dec 2009

Poisson DistributionDownload/ViewStudents are required to identify and denote a poisson distribution, determine the probability using GC, evaluate mean of poisson using either GC or formula if not provided and use E(X)= Var(X)= mean of poisson. Also, students must know the conditions for using Normal approximations.

Last Updated: Feb 2010

Normal DistributionDownload/ViewStudents are required to evaluate normal probability using GC, evaluate mean and variance using either GC or formula if not provided and recall the properties for determining mean and variance of normal distribution such as E(nX)=nE(X), Var(nX)=(n^2)Var(X) etc. Also, students must apply Normal approximations to appropriate situations.

Hypothesis TestingDownload/ViewStudents are required to apply all standard steps in hypothesis testing, evaluate p-value using GC & provide appropriate conclusion and solve for unknown parameters such as mean, variance, sample size and/or level of significance if they are not provided. H2 students must apply z-test & t-test to appropriate situations.

Last Updated: Feb 2010

Correlation & Linear RegressionDownload/ViewStudents are required to use GC to evaluate r & least square regression equations and plot scatter diagram. Students must differentiate between extrapolation (i.e. not accurate) & interpolation (i.e. accurate) when using regression equations. Students should refer to MF15 for relevant formulas.